### Schedule:

Past lecures:

Lecture 1. Very basic
properties of free groups

Lectures 2-3. Nielsen-Schreier Theorem (subgroups of
free groups are free).

Lectures 4-5. Presentations of groups by generators
and relations. Finitely and infinitely presented groups.

Lecture 6. Residually
finite groups

Lectures 7-8. Automorphism groups of free groups.

Lecture 9. Free
products

Lecure 10. Amalgams
(briefly) and HNN-extensions.

Lecture 11. Word growth in groups.
Examples and overview.

Lectures 12-13. Nilpotent groups have polynomial growth (Wolf's
theorem).

Lecture 14. Growth in
solvable groups (Milnor-Wolf theorem)

Lecture 15. Free Lie
algebras.

Lectures 16-17. Lie and associative rings corresponding to groups

Lecture 18. Burnside
problems. Puchta's construction.

Lectures 19-20. Golod-Shafarevich inequality and
Golod-Shafarevich groups.

Lecture 21. Linear
groups. Burnside problem for linear groups.

Lecture 22.
General Burnside problem for linear groups. Kolchin theorem.

Lecture 23.
Zariski topology. Lie-Kolchin theorem.

Upcoming lecures (plan):

Lecture 24.
Malt'sev theorem (finitely generated linear groups are
residually finite).